100 people were asked whether they had visited France (F) or Spain (S) - OCR - GCSE Maths - Question 10 - 2023 - Paper 4

To find the probability that a randomly chosen person had visited exactly one of the countries, we need to consider the people who visited only France and those who visited only Spain:

• People who visited only France: 36
• People who visited only Spain: 41

Total who visited exactly one country = 36 + 41 = 77.

The probability is given by:

$P(\text{exactly one}) = \frac{\text{Number of people who visited exactly one country}}{\text{Total number of people}} = \frac{77}{100} = 0.77$

To find the probability that the person had visited France given that they had visited Spain, we use conditional probability:

Let A be the event that the person visited France and B be the event that the person visited Spain. We need to find:

$P(A|B) = \frac{P(A \cap B)}{P(B)}$

From our earlier findings:

• Probability of visiting both France and Spain, $P(A \cap B) = \frac{19}{100}$.
• Probability of visiting Spain, $P(B) = \frac{60}{100}$.

Thus, we can calculate:

$P(A|B) = \frac{\frac{19}{100}}{\frac{60}{100}} = \frac{19}{60} \approx 0.3167$